Method for measuring shear wave velocity of material

Abstract

The invention discloses a method for measuring the shear wave velocity of a material, which comprises the following steps of: firstly, selecting a material to be tested, and manufacturing the material into a cylindrical test piece; pasting a sensor on the cylindrical surface at each of the two ends of the cylindrical test piece, wherein the two sensors are spatially staggered to form an included angle of 90 degrees; then electrically connecting one sensor with a signal generator, electrically connecting the other sensor with a lock-in amplifier, electrically connecting the lock-in amplifier with signal acquisition equipment, and starting the signal generator and the signal acquisition equipment; performing signal analysis to obtain a response frequency spectrum of the cylindrical test piece under scanning excitation; and finally extracting a first-order torsional natural vibration frequency corresponding to a first peak value in the response frequency spectrum, and calculating to obtain the shear wave velocity of the test piece. According to the method, the selection error of the first arrival moment of the shear wave and the influence caused by ultrasonic time domain measurement noise can be avoided, the convenience and accuracy of material shear wave velocity measurement are improved, and a theoretical basis and data support can be provided for measurement of related mechanical properties of the material.

Description

Technical Field

[0001] The invention relates to a method for measuring the wave velocity of a material under stress, in particular to a method for measuring the shear wave velocity of a material, and belongs to the technical field of material science. Background Art

[0002] In the field of materials science, the measurement of compression wave and shear wave velocity of materials is an important way to determine the Poisson's ratio elastic constant, shear modulus, bulk modulus and Young's modulus of materials. In terms of material performance evaluation, the shear wave velocity of materials is an important indicator reflecting the elastic properties and mechanical behavior of materials. By measuring the shear wave velocity of materials, the mechanical properties such as shear strength and toughness of materials can be evaluated, providing an important basis for the selection and application of materials. In terms of material quality testing, during the material production process, the measurement of shear wave velocity can also be used to detect internal defects and damage of materials. By comparing the shear wave velocities of different materials, small changes and differences within them can be found, so as to timely discover and solve quality problems.

[0003] The traditional wave velocity measurement method mainly uses ultrasonic probes in the time domain to calculate by measuring the propagation distance and propagation time of the wave. Since the compression wave is the first wave to arrive, its first arrival time is very easy to determine, so the measurement of the compression wave velocity is also the easiest. However, the shear wave is the wave that arrives later. When the propagation distance is far, it is separated from the compression wave and is relatively easy to determine. However, when the specimen size is small and the propagation distance is very short, the first arrival time of the shear wave is often difficult to determine because it is integrated into the entire waveform. In addition, the noise during measurement also greatly increases the difficulty of identifying the first arrival time of the shear wave.

[0004] There is currently a method to approximately infer the shear wave velocity through the surface wave velocity. It is believed that the shear wave velocity is approximately equal to the surface wave velocity / 0.87. However, this method is an approximate method and is also affected by the Poisson's ratio and elastic modulus of the material. Summary of the invention

[0005] In response to the problems existing in the above-mentioned prior art, the present invention provides a method for measuring the shear wave velocity of materials, which can avoid the error in selecting the first arrival time of the shear wave and the influence of ultrasonic time domain measurement noise, improve the convenience and accuracy of material shear wave velocity measurement, and provide a theoretical basis and data support for the measurement of material-related mechanical properties.

[0006] To achieve the above purpose, the method for measuring the shear wave velocity of the material specifically includes the following steps:

[0007] Step 1, select the material to be tested and make it into a cylindrical specimen;

[0008] Step 2, affix a sensor to the cylindrical surface at both ends of the cylindrical specimen, and the two sensors are staggered at a 90° angle;

[0009] Step 3, electrically connect one sensor to the signal generator, electrically connect another sensor to the phase-locked amplifier, and electrically connect the phase-locked amplifier to the signal acquisition device, start the signal generator and the signal acquisition device, emit a continuous scanning signal through the signal generator, and the signal acquisition device synchronously acquires the signal;

[0010] Step 4, perform signal analysis to obtain the response spectrum of the cylindrical specimen under scanning excitation;

[0011] Step 5: Extract the first-order torsional natural frequency f corresponding to the first peak in the response spectrum. t , the shear wave velocity of the specimen is calculated, and the calculation formula is as follows:

[0012] V s =2Lf t

[0013] Where: V s is the shear wave velocity; L is the axial length of the cylindrical specimen; f t is the first-order torsional natural frequency corresponding to the first peak.

[0014] Furthermore, in Step 1, the ratio of the axial length dimension L to the diameter dimension D of the cylindrical specimen is in the range of 0.9 to 1.90.

[0015] Furthermore, in Step 2, before attaching the sensor to the cylindrical specimen, the weight m1 of the cylindrical specimen is measured and recorded, and the weight m2 of the sensor is measured and recorded, and m2 does not exceed 1% of m1.

[0016] Furthermore, in Step 2, after the sensors are attached to both ends of the cylindrical specimen, the cylindrical specimen is placed flat on the sponge pad.

[0017] Furthermore, in Step 4, the collected original trigger signal and response signal are first plotted, and then the trigger point position in the trigger signal is matched with the data position in the original spectrum, and the original spectrum is normalized using the maximum value of the response to obtain the normalized response spectrum of the cylindrical specimen under scanning excitation.

[0018] Compared with the prior art, the material shear wave velocity measurement method is easy to operate and has high measurement accuracy, and has the following beneficial effects:

[0019] 1. The frequency domain method is used to measure the frequency related to the shear wave velocity, and there is no need to extract the first arrival time of the shear wave, which can greatly improve the convenience and accuracy of the test.

[0020] 2. By setting the ratio range of the axial length and diameter of the specimen, it is ensured that the first identified frequency is the frequency related to the shear wave velocity, thus ensuring the accuracy of the measurement.

[0021] 3. By limiting the ratio of the mass of the sensor to the mass of the test piece, the error caused by the sensor's own weight on the test frequency can be reduced.

[0022] 4. By placing the specimen flat on the sponge pad, on the one hand, the test instability caused by placing the specimen upright or tilted in traditional testing can be avoided; on the other hand, the additional constraints on the specimen can be significantly reduced by placing the sponge pad, ensuring the accuracy of the specimen's free vibration and frequency measurement.

[0023] 5. The asymmetric arrangement of the sensors can effectively ensure the excitation of the first frequency related to the shear wave velocity, thereby ensuring the accuracy of the measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a diagram showing the variation of the first-order natural frequency with the aspect ratio of the cylindrical specimen;

[0025] Figure 2 is a diagram showing that the test piece of the present invention is placed flat on a sponge pad after being attached to the sensor;

[0026] Figure 3 It is a diagram showing the excitation and acquisition connections of the test piece of the present invention;

[0027] Figure 4 is a diagram showing the original trigger signal of the test piece of the present invention;

[0028] Figure 5 is a diagram showing the original response signal of the test piece of the present invention;

[0029] Figure 6 is a normalized response spectrum diagram of the test piece of the present invention;

[0030] Figure 7 It is a diagram showing the traditional ultrasonic velocity measurement along the length direction of the specimen using a special shear wave sensor;

[0031] Figure 8 is the signal time domain diagram of the shear wave sensor;

[0032] Fig. 9 is a diagram showing ultrasonic measurement using a compression wave sensor;

[0033] Fig.10 is the signal time domain diagram of the compression wave sensor;

[0034] Fig.11 is a diagram showing ultrasonic measurement using a piezoelectric wafer sensor;

[0035] Fig.12 It is the time domain diagram of the signal of the piezoelectric chip sensor. DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings.

[0037] The method for measuring the shear wave velocity of the material specifically comprises the following steps:

[0038] Step 1, select the material to be tested and make it into a cylindrical specimen.

[0039] If the specimen size is not appropriate, the first-order bending natural frequency of the specimen perpendicular to the axial or radial direction may be lower than the first-order shear modal frequency required by the present invention, resulting in errors in directly selecting the first main frequency from the spectrum for shear wave velocity calculation.

[0040] The first-order bending natural frequency f of the cylindrical specimen perpendicular to the axial direction b It is expressed as follows:

[0041]

[0042] Where: k1 is the first-order bending modal constant perpendicular to the axial direction, which is 4.730041; E is the elastic modulus of the material; ρ is the material density.

[0043] The first-order bending natural frequency f of the cylindrical specimen perpendicular to the radial direction p It is expressed as follows:

[0044]

[0045] Where: β1 is the first-order bending modal constant perpendicular to the radial direction, β1 is related to the Poisson's ratio μ of the material, when μ=0.3, β1=3.00052.

[0046] The first-order torsional natural frequency f of the cylindrical specimen t (The detailed derivation process can be seen in the subsequent step 6) is expressed as follows:

[0047]

[0048] Where: G is the shear modulus of the material.

[0049] Set μ = 0.3 and plot the first-order frequencies of a series of cylindrical specimens under different L / D conditions, and use the first-order torsional natural frequency f t Normalizing it, we can get the changes of different modal frequencies as follows: Figure 1As shown in the figure, it can be seen that when μ = 0.3, only when the aspect ratio is within a certain limited range (0.42 ~ 2.87), the first-order torsional natural frequency f t It will be the smallest among all kinds of first-order natural frequencies. Considering that the variation range of Poisson's ratio of conventional solid materials usually varies between 0.10 and 0.40, and in order to make the test interval as far away as possible from the corresponding frequency at the intersection, the present invention limits the aspect ratio range of the cylindrical specimen to 0.9 to 1.90, so as to fully avoid other interfering frequency bands and ensure that the first-order mode of the specimen is a torsional mode, which can ensure that the first identified frequency is the frequency related to the shear wave velocity, and ensure the accuracy of the measurement.

[0050] In the test embodiment, the material to be tested is selected as concrete, which is made into a cylindrical test piece, whose axial length dimension L is 3.756 cm, and diameter dimension D is 2.468 cm, and D:L=1.52.

[0051] Step 2, measure and record the weight m1 of the specimen, and measure and record the weight m2 of the sensor. m2 should not exceed 1% of m1. The sensor can be a piezoelectric piece or other ultrasonic probe.

[0052] There is usually the following relationship between the natural frequency f of a cylindrical specimen and its mass m1:

[0053]

[0054] According to the relative error formula ( It can be seen that when the weight m2 of the sensor attached to the cylindrical specimen does not exceed 1% of the weight m1 of the cylindrical specimen, the relative error caused by this is less than 0.5%. At this time, the frequency measurement error caused by the additional mass is negligible. Therefore, the present invention stipulates that m2 should not exceed 1% of m1 to reduce the error influence of the sensor's own weight on the test frequency.

[0055] The weight m1 of the test piece of the test embodiment is 43.02 g, and the weight m2 of the sensor is 0.18 g. It is calculated that m2 / m1=0.42%, which does not exceed 1% of the weight of the test piece.

[0056] Step 3, stick a sensor on the cylindrical surface at both ends of the specimen, and the two sensors are staggered at a 90° angle, and then place the specimen flat on the sponge pad.

[0057] Test Example After the test piece is attached to the sensor, it is placed flat on the sponge pad. Figure 2 shown.

[0058] Step 4, such as Figure 3As shown, one sensor is electrically connected to a signal generator, another sensor is electrically connected to a phase-locked amplifier, and the phase-locked amplifier is electrically connected to a signal acquisition device. The signal generator and the signal acquisition device are started, a continuous scanning signal is emitted by the signal generator, and the signal acquisition device synchronously acquires the signal.

[0059] The excitation and acquisition parameters of the test specimens of the test embodiment are shown in Table 1 below:

[0060] Table 1 Excitation and acquisition parameters

[0061]

[0062]

[0063] Step 5, perform signal analysis to obtain the response spectrum of the specimen under scanning excitation.

[0064] For the test sample of the test embodiment, firstly draw the collected original trigger signal and response signal as shown in Figure 4 , Figure 5 As shown, then set the trigger point position in the trigger signal ( Figure 3 The data point 203677 at the vertical line position in the figure corresponds to the data position in the original spectrum, and the original spectrum is normalized using the maximum value of the response to obtain the normalized response spectrum of the specimen under scanning excitation as shown in Figure 6 shown.

[0065] Step 6, extract the frequency f1 corresponding to the first peak in the response spectrum and calculate the shear wave velocity of the specimen.

[0066] The propagation of waves in a medium can be explained by the relationship between strain and displacement:

[0067] Strain-displacement relationship: The relationship between the displacement u(x, t) of the material and the strain ε is expressed as follows:

[0068]

[0069] Stress-strain relationship: During torsion of an elastic material, the relationship between the shear stress τ and the shear strain ε is described by the shear modulus G as follows:

[0070] τ=Gε

[0071] Formula ②

[0072] Balance of force: Consider the balance of force per unit volume. Assuming that the shear force per unit length is τ and the density of the material is ρ, we have:

[0073]

[0074] Substituting equation ② into equation ③, we can get

[0075]

[0076] Substituting equation ① into equation ④, we can get

[0077]

[0078] Formula ⑤ can be rewritten as

[0079]

[0080] Dividing both sides of equation ⑥ by ρ and rearranging, we can obtain the wave equation:

[0081]

[0082] Solve the wave equation of the above equation ⑦, assuming that the solution of the displacement is in the form of separated variables, that is,

[0083] u(x,t)=X(x)T(t) Formula⑧

[0084] Substituting equation ⑧ into the wave equation of equation ⑦, we can obtain:

[0085]

[0086] Dividing both sides of equation 9 by XT yields:

[0087]

[0088] Where: λ is the separation constant.

[0089] The time part of the equation is expressed as:

[0090]

[0091] The solution is:

[0092]

[0093] In the formula: A and B are constants.

[0094] The equation for the spatial part is expressed as:

[0095]

[0096] The solution is:

[0097]

[0098] Where: C and D are constants.

[0099] Pair Apply boundary conditions. For a freely vibrating cylinder, the boundary conditions are that both ends are free (displacement is 0), that is, X(0) = 0, X(L) = 0. From X(0) = 0, we can get C = 0, so For X(L) = 0, we can get The above formula is always true, which means: Right now For the first-order mode n=1, we have

[0100] Will Substitution The solution for the time part is:

[0101]

[0102] From this, we can get the corresponding first-order torsional natural frequency f t for:

[0103]

[0104] Then we can get:

[0105] V s =2Lf t Mode

[0106] Where: V s is the shear wave velocity; L is the axial length of the cylindrical specimen; f t is the first-order torsional natural frequency corresponding to the first peak.

[0107] For the test specimen of the embodiment, the first-order torsional natural frequency f corresponding to the first peak in the response spectrum is extracted. t is 35.47kHz, using The calculated shear wave velocity of the specimen is 2664.51 m / s.

[0108] In order to verify the accuracy of the shear wave velocity of the test specimen, a special shear wave sensor was used to perform conventional ultrasonic velocity measurement in the axial length direction of the specimen. Figure 7 The excitation and acquisition parameters are shown in Table 2 below:

[0109] Table 2 Ultrasonic excitation and acquisition parameters

[0110] Excitation and acquisition parameters Numeric Excitation frequency 500kHz Excitation Amplitude 100V Acquisition trigger type Edge Trigger level 1V Amplifier Gain 20dB Signal acquisition frequency 10MHz Signal acquisition time 0.001s Number of sampling points 10000

[0111] The ultrasonic response signal obtained is as follows Figure 8 As shown in Figure 2, although the dedicated shear wave sensor has fully suppressed the compression wave, it is noted that Figure 8 The compression wave signal still exists, and the first signal to arrive is t P=0.079ms is the compression wave signal, Figure 8 The time of the first arrival of the shear wave in is t s = 0.0142ms, through Vs = L / t s The calculated shear wave velocity is 2645.07 m / s, which is highly consistent with the shear wave velocity 2664.51 m / s obtained by the method proposed in the present invention, with a relative error of 0.73%.

[0112] Figures 9 to 12 The arrangement and ultrasonic response signal of ultrasonic measurement using compression wave sensor and piezoelectric chip are also given. Fig. 9 and Fig.12 It can be seen from the signal time domain diagram in that the compression wave head of the specimen is clearly discernible at the time, but the arrival time of the shear wave is basically indistinguishable from the waveform diagram, and the wave velocity of the shear wave cannot be directly obtained at this time.

[0113] Compared with the time domain measurement method used in traditional wave velocity measurement, the measurement method of shear wave velocity of this material does not need to extract the first arrival time of the shear wave, thereby avoiding the error in the selection of the first arrival time of the shear wave and the influence of ultrasonic time domain measurement noise. It can greatly improve the convenience and accuracy of material shear wave velocity measurement, and provide a theoretical basis and data support for the measurement of material-related mechanical properties.

Claims

1. A method for measuring shear wave velocity of a material, characterized in that: The specific steps include: Step 1, select the material to be tested and make it into a cylindrical specimen; Step 2, affix a sensor to the cylindrical surface at both ends of the cylindrical specimen, and the two sensors are staggered at a 90° angle; Step 3, electrically connect one sensor to the signal generator, electrically connect another sensor to the phase-locked amplifier, and electrically connect the phase-locked amplifier to the signal acquisition device, start the signal generator and the signal acquisition device, emit a continuous scanning signal through the signal generator, and the signal acquisition device synchronously acquires the signal; Step 4, perform signal analysis to obtain the response spectrum of the cylindrical specimen under scanning excitation; Step 5: Extract the first-order torsional natural frequency f corresponding to the first peak in the response spectrum. t , the shear wave velocity of the specimen is calculated, and the calculation formula is as follows: <h2 style=";text-align:left;direction:ltr">V<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> <2Lf<h2 style=";text-align:left;direction:ltr"> t Where: V s is the shear wave velocity; L is the axial length of the cylindrical specimen; f t is the first-order torsional natural frequency corresponding to the first peak.

2. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 1, the ratio of the axial length dimension L to the diameter dimension D of the cylindrical specimen is in the range of 0.9 to 1.

90.

3. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 2, before attaching the sensor to the cylindrical specimen, measure and record the weight m1 of the cylindrical specimen, and measure and record the weight m2 of the sensor, and m2 shall not exceed 1% of m1.

4. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 2, after attaching sensors to both ends of the cylindrical specimen, place the cylindrical specimen flat on the sponge pad.

5. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 4, the collected original trigger signal and response signal are first plotted, and then the trigger point position in the trigger signal is matched with the data position in the original spectrum, and the original spectrum is normalized using the maximum value of the response to obtain the normalized response spectrum of the cylindrical specimen under scanning excitation.

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